LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

ADDITION OF ALGEBRAIC EXPRESSION OF UNLIKE TERM WITH SAME VARIABLE & DIFFERENT POWER

__ADDITION OF UNLIKE TERM WITH SAME VARIABLE & DIFFERENT POWER -__

**When adding algebraic expressions with unlike terms that contain the same variables but with different exponents, you can't directly combine these terms because they represent different powers of the same variable. However, you can simplify the expression by grouping terms with the same variables and then expressing the result in its simplest form. Here's how to do it step by step:**

__Identify Like Variables:-__Examine the expressions and identify terms with the same variables, even if the exponents are different.__Group Terms by Variables:-__Organize the terms into groups based on their common variables. Each group may contain terms with the same variable but different exponents.__Combine Terms Within Each Group:-__For each group of terms with the same variable(s), combine them by adding or subtracting the coefficients, keeping the variable(s) and their exponents unchanged.__Write the Result:-__Express the final result as a sum of the combined groups.

**Here's an example of adding algebraic expressions with unlike terms that have the same variable but different exponents:**

**Example.1) Adding Expressions with Different Exponents**

**Given the expressions:**

**3x²+ 2x - 5x³****2x⁵- 4x²+ 1**

**Ans.)**

**Identify like variables and group the terms:**

__Group 1:-__3x² and -4x² (both contain the variable "x²").

__Group 2:-__2x and 0 (there is no "x" term in the second expression).

.__Group 3:-__-5x³, 2x⁵, and 1 (these terms contain different powers of "x")

**Combine terms within each group:**

__Group 1:-__3x²- 4x² = -x².

__Group 2:-__2x + 0 = 2x.

__Group 3:-__-5x³+ 2x⁵ + 1 (no further simplification possible within this group).

**Write the result as a sum of the combined groups:**

**(-x²) + (2x) + (-5x³+ 2x⁵ + 1)**

**So, the simplified expression with unlike terms that have the same variable but different exponents is:
2x⁵ - 5x³- x²+ 2x + 1.**

**Example.2) Adding Expressions with Variables of Different Powers**

**Given the expressions:**

**3x²+ 2x - 5x³****4x - x²+ 7x³**

**Ans.)**

**Identify and group similar terms:**

__Group 1:-__3x² and -x² (both involve the variable "x" with different exponents).

__Group 2:-__2x and 4x (both involve the variable "x" with different exponents).

__Group 3:-__-5x³ and 7x³ (both involve the variable "x" with different exponents).

**Now, combine the like terms within each group:**

__Group 1:-__3x²- x²= 2x².

__Group 2:-__2x + 4x = 6x.

__Group 3:-__-5x³+ 7x³= 2x³.

**Write the result as a sum of the combined terms and any remaining terms:**

**2x²+ 6x + 2x³.**

**So, the simplified expression with unlike terms that contain the same variables with different powers is 2x²+ 6x + 2x³.**

**"Unlike terms" are terms that contain the same variables
having different power.**

**7x²y⁵ and -2x³y⁵ These are NOT like terms since the exponents on x are different. These are unlike terms.**

**3.) 5a², 19b², c²**

**= 5a²+ 19b²+ c²**

**(All are unlike terms so we cannot
add their coefficients)**

**4.) Add: 11a²+ 8b²- 9c², 5b²+ 3c²- 4a² and 3a²- 4b²- 4c².**

**Ans.)**

**Writing the terms of the given
expressions in the same order in form of rows with like terms below each other
and adding column wise;**

** 11a²+ 8b²- 9c²**

** - 4a²+ 5b²+ 3c² **

** 3a²- 4b²- 4c²**

**
**

** ------------------**

** 10a²+ 9b²- 10c²**

**In this example, we combined the terms with the same variable "x" but different exponents, resulting in a simplified expression with like terms.**